Question

PLEASE HELP!!!!

In ΔRST shown below, segment SU is an altitude:



What property or definition is needed to prove that ΔRUS is similar to ΔSUT? (5 points)


Transitive Property of Equality

Reflexive Property of Equality

Definition of Supplementary Angles

Definition of Congruence

Answer 1

The correct answer to this question is the Definition of Congruence.

(last option)

Explanation:

Just took the test (: good luck !

Answer 2

∴ Δ RUS ~ ΔSUT ....Transitive Property of Equality .

Explanation:

In ΔRST and Δ RUS

∠R ≅ ∠R ……….{Reflexive Property}

∠S ≅ ∠U ……….{ Measure of each angle 90°}

Δ RST ~ ΔRUS ….{By Angle-Angle Similarity test} .......( 1 )

Similarly,

In ΔRST and Δ SUT

∠T ≅ ∠T ……….{Reflexive Property}

∠S ≅ ∠U ……….{ Measure of each angle 90°}

Δ RST ~ ΔSUT ….{By Angle-Angle Similarity test} .......( 2 )

Transitive Property of Equality.

The property state :

If a = b and b = c, then a = c.

Therefore,

Δ RST ~ ΔRUS ….{By Angle-Angle Similarity test} .......( 1 )

Δ RST ~ ΔSUT ….{By Angle-Angle Similarity test} .......( 2 )

∴ Δ RUS ~ ΔSUT ....Transitive Property of Equality